We studied the temperature and magnetic field dependence of vortex dissipation and critical current in the mixed-state of unconventional superconducting alloys Ba(Fe1−xCox)2As2 (0.044 ≤ x ≤ 0.100) through current-voltage measurements. Our results reveal that all the electric field E vs current density j curves in the Ohmic regime merge to one point (j0, E0) and that there is a simple relationship between the critical current density jc and flux-flow resistivity ρ ff : ρ ff /ρn = (1 − jc/j0) −1 , where ρn = E0/j0 is the normal-state resistivity just above the superconducting transition. In addition, E0 is positive for all five dopings, reflecting the abnormal behavior of the flux-flow resistivity ρ ff : it increases with decreasing magnetic field. In contrast, E0 is negative for the conventional superconductor Nb since, as expected, ρ ff decreases with decreasing magnetic field. Furthermore, in the under-doped and over-doped single crystals of Ba(Fe1−xCox)2As2, the parameter E0 remains temperature independent, while it decreases with increasing temperature for the single crystals around optimal doping (0.060 ≤ x ≤ 0.072). This result points to the co-existence of superconductivity with some other phase around optimal doping.